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CMA Final · Strategic Cost Management · Business Forecasting Models - Time Series and Regression Analysis

For five periods, a Chennai firm finds ΣX = 15, ΣY = 60, ΣXY = 205 and ΣX² = 55, where X is the period number. Using least squares, what is the slope b of the trend line Y = a + bX?

The slope is (1025 − 900)/(275 − 225) = 125/50 = 2.5 units per period, using the least squares normal equation formula.

  1. A2.5Correct
  2. B3.0
  3. C4.5
  4. D2.0

Explanation

b = (nΣXY − ΣXΣY)/(nΣX² − (ΣX)²) = (5x205 − 15x60)/(5x55 − 225) = (1025 − 900)/50 = 2.5. Option 4.5 is the intercept a = (60 − 37.5)/5, not the slope.

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